Standard DMD exploits the low-rank structure of \(A\)  to efficiently perform diagnostics on the learned model.
Some of the manifolds we consider (such as circulant, tridiagonal, upper triangular) do not have an obvious
or useful low-rank approximation.
Instead, these matrices often have an alternative structure that can be exploited to perform fast diagnostic tests.
For example, tridiagonal matrices rarely have a meaningful low-rank approximation, but nevertheless admit a fast
eigendecomposition and singular value decomposition [1]}.
